1. preference statements
D E C I S I O N T H E O R Y
Preference Programming
Ratio-based Efficiency Analysis
Interval goal programming
incomplete information
comparison of DMUs under incomplete information
about the output and input weights
extension of a goal point to a goal set
in value tree analysis
Goal point: (g1,g2)
Goal set (intervals): ([l1,u1],[l2,u2])
Consistent ?
Add new / revise
preference statements no
Recommendations
by “decision rules”
Overall value and
ranking intervals
Dominance
relations
Interpretation
of results
Display of results and
recommendations
Adequate ?
yes
Decision x2 x2
u1/u2
0.5 1 E1 E2 E3 E4 E* E0
E1 / E*=1
E1 / E*=0.6
E1 / E*[0.6,1.0]
E2 / E*[0.9,1.0]
...
E3 / E0[1.2,1.6]
E4 / E0[1.0,1.3]
E3 / E0 = 1.2
E3 / E0 = 1.6 x* x* S S
DMU1
DMU3
DMU2
DMU4
DMU1
DMU3
DMU2
DMU4
ranking 1
ranking 2
ranking 3
ranking 4 x1 x1
new flexibility in dynamic problems
time x t1 t2 t3 tk
efficiency bounds
dominance relations
attainable rankings
interval methods:
Preference Assessment by Imprecise
Ratio Statements (PAIRS)
Interval AHP
Preference Ratios in Multiattribute Evaluation (PRIME)
Interval SMART/SWING
sensitivity of university rankings
- what if slightly different weigths were applied?
global sensitivity analysis
exact weights
20 % interval
30 % interval
incomplete ordinal
no information
Robust rankings
”Different weighting would
likely yield a better ranking”
10th
442nd
Alternative
Strategy 0
Strategy 1
Strategy 2
Strategy 3
Strategy 4
Utility
0.474
0.697
0.694
0.748
0.628
Costs
Other cancers
Political cost
Soc.-Psych Negative
Soc.-Psych Positive
Thyroid cancer
incomplete ordinal information:
Rank Inclusion in Criteria Hierarchies (RICH)
RICHER = RICH with Extended Rankings
origins of procedural and behavioral biases
Number of attribute
levels effect in
conjoint analysis
Splitting bias
Rank reversal in
AHP
Averages over a
group yield even
weights
Normalization
Weights derived from ordinal infromation
Division of attributes changes weights
Range effect
Hierarchical
weighting leads to
steeper weigths
Weighting methods
yield different
web-sites and selected publications
A. Salo and A. Punkka: Ranking intervals and dominance relations for Ratio-based Efficiency Analysis, manuscript, 2010
A. Punkka and A. Salo: Preference Programming with incomplete ordinal information, manuscript, 2010
A. Salo and R. P. Hämäläinen: Preference Programming - multicriteria weighting models under incomplete information,
in: Zopounidis and Pardalos (eds.): Handbook of Multicriteria Decision Analysis, Springer, New York, 2010
J. Liesiö, P. Mild and A. Salo: Preference programming for robust multi-criteria portfolio modeling and project selection,
Eur. J. Oper. Res. (EJOR), 2007
J. Mustajoki, R. P. Hämäläinen and M. R. K. Lindstedt: Using intervals for global sensitivity and worst case analyses in multiattribute value trees, EJOR, 2006
A. Salo and A. Punkka: Rank inclusion in criteria hierarchies, EJOR, 2005
J. Mustajoki, R. P. Hämäläinen and A. Salo: Decision Support by Interval SMART/SWING - Incorporating Imprecision in the SMART and SWING Methods,
Decision Sciences, 2005
A. Salo and R. P. Hämäläinen: Preference ratios in multiattribute evaluation (PRIME), IEEE Syst. Man Cybernetics, 2001
R. P. Hämäläinen and J. Mäntysaari: A dynamic interval goal programming approach to the regulation of a lake-river system, J. Multi-Crit. Dec. Anal., 2001
A. Salo and R. P. Hämäläinen: Preference programming through approximate ratio comparisons, EJOR, 1995
A. Salo and R. P. Hämäläinen: Preference assessment by imprecise ratio statements, Operations Research, 1992
Updated
Systems
Analysis Laboratory